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href="javascript:void(0);"><i class="fas fa-bars fa-fw"></i></a></div></div></nav><div id="post-info"><h1 class="post-title">C++代码示例：排列数简单生成工具</h1><div id="post-meta"><div class="meta-firstline"><span class="post-meta-date"><i class="far fa-calendar-alt fa-fw post-meta-icon"></i><span class="post-meta-label">发表于</span><time class="post-meta-date-created" datetime="2023-10-01T12:19:23.000Z" title="发表于 2023-10-01 20:19:23">2023-10-01</time><span class="post-meta-separator">|</span><i class="fas fa-history fa-fw post-meta-icon"></i><span class="post-meta-label">更新于</span><time class="post-meta-date-updated" datetime="2024-02-28T02:52:21.965Z" title="更新于 2024-02-28 10:52:21">2024-02-28</time></span><span class="post-meta-categories"><span class="post-meta-separator">|</span><i class="fas fa-inbox fa-fw post-meta-icon"></i><a class="post-meta-categories" href="/categories/C/">C++</a></span></div><div class="meta-secondline"><span class="post-meta-separator">|</span><span class="post-meta-pv-cv" id="" data-flag-title="C++代码示例：排列数简单生成工具"><i class="far fa-eye fa-fw post-meta-icon"></i><span class="post-meta-label">阅读量:</span><span id="busuanzi_value_page_pv"><i class="fa-solid fa-spinner fa-spin"></i></span></span></div></div></div></header><main class="layout" id="content-inner"><div id="post"><article class="post-content" id="article-container"><h1 id="前言"><a href="#前言" class="headerlink" title="前言"></a>前言</h1><p>C++代码示例：排列数简单生成工具。</p>
<hr>
<h1 id="代码仓库"><a href="#代码仓库" class="headerlink" title="代码仓库"></a>代码仓库</h1><ul>
<li><a target="_blank" rel="noopener" href="https://github.com/yezhening/Programming-examples">yezhening&#x2F;Programming-examples: 编程实例 (github.com)</a></li>
<li><a target="_blank" rel="noopener" href="https://gitee.com/yezhening/Programming-examples">Programming-examples: 编程实例 (gitee.com)</a></li>
</ul>
<hr>
<h1 id="内容"><a href="#内容" class="headerlink" title="内容"></a>内容</h1><ul>
<li>简单地生成排列数</li>
<li><strong>有详细的步骤解析</strong></li>
</ul>
<hr>
<h1 id="代码（有详细注释）"><a href="#代码（有详细注释）" class="headerlink" title="代码（有详细注释）"></a>代码（有详细注释）</h1><p>cpermutation.cpp</p>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br><span class="line">136</span><br><span class="line">137</span><br><span class="line">138</span><br><span class="line">139</span><br><span class="line">140</span><br><span class="line">141</span><br><span class="line">142</span><br><span class="line">143</span><br><span class="line">144</span><br><span class="line">145</span><br><span class="line">146</span><br><span class="line">147</span><br><span class="line">148</span><br><span class="line">149</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;vector&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;iostream&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;unordered_set&gt;</span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> std::cout;</span><br><span class="line"><span class="keyword">using</span> std::endl;</span><br><span class="line"><span class="keyword">using</span> std::unordered_set;</span><br><span class="line"><span class="keyword">using</span> std::vector;</span><br><span class="line"></span><br><span class="line"><span class="keyword">class</span> <span class="title class_">CPermutation</span></span><br><span class="line">&#123;</span><br><span class="line"><span class="keyword">public</span>:</span><br><span class="line">    <span class="built_in">CPermutation</span>(<span class="type">const</span> <span class="type">int</span> &amp;n, <span class="type">const</span> <span class="type">int</span> &amp;m) : <span class="built_in">n</span>(n), <span class="built_in">m</span>(m), <span class="built_in">flags</span>(<span class="number">0</span>), <span class="built_in">curPerm</span>(<span class="number">0</span>), <span class="built_in">permCount</span>(<span class="number">0</span>) &#123;&#125;</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="type">bool</span> <span class="title">next</span><span class="params">()</span></span></span><br><span class="line"><span class="function">    </span>&#123;</span><br><span class="line">        <span class="comment">// 第一次进入初始化当前排列，如m=3，this-&gt;curPerm为012，从012开始遍历</span></span><br><span class="line">        <span class="keyword">if</span> (<span class="keyword">this</span>-&gt;curPerm.<span class="built_in">empty</span>() == <span class="literal">true</span>)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i &lt; <span class="keyword">this</span>-&gt;m; ++i)</span><br><span class="line">            &#123;</span><br><span class="line">                <span class="keyword">this</span>-&gt;curPerm.<span class="built_in">push_back</span>(i);</span><br><span class="line">                <span class="keyword">this</span>-&gt;flags.<span class="built_in">insert</span>(i); <span class="comment">// 记录哈希</span></span><br><span class="line">            &#125;</span><br><span class="line"></span><br><span class="line">            ++<span class="keyword">this</span>-&gt;permCount;</span><br><span class="line">            <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="comment">// 1. 首先，确定某个位置是否已经达到了当前意义下的“最大值”—“当前” 的意义：前面的位置数值固定之后</span></span><br><span class="line">        <span class="comment">// 求当前位置应当的最大值</span></span><br><span class="line">        <span class="comment">// 注意理解：如014，索引2位置可取23，最大值为3；索引1位置可取234，最大值为4；索引0位置可取1234，最大值为4，左边位置的取值范围要包括右边的位置</span></span><br><span class="line">        <span class="comment">// 从后往前大到小遍历，如果这个数不在哈希表中就是应该的最大值</span></span><br><span class="line"></span><br><span class="line">        <span class="comment">// 2. 然后，从后向前寻找第一个不是当前最大值的位置</span></span><br><span class="line">        <span class="comment">// 修正：小于当前应当最大值的位置</span></span><br><span class="line">        <span class="comment">// 如014，则求得的位置是索引1</span></span><br><span class="line">        <span class="type">int</span> curPos = <span class="keyword">this</span>-&gt;m - <span class="number">1</span>;</span><br><span class="line">        <span class="type">int</span> curMax = <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">while</span> (curPos &gt;= <span class="number">0</span>)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="comment">// 1.</span></span><br><span class="line">            <span class="keyword">for</span> (<span class="type">int</span> i = <span class="keyword">this</span>-&gt;n - <span class="number">1</span>; i &gt;= <span class="number">0</span>; --i)</span><br><span class="line">            &#123;</span><br><span class="line">                <span class="keyword">if</span> (flags.<span class="built_in">find</span>(i) == flags.<span class="built_in">end</span>())</span><br><span class="line">                &#123;</span><br><span class="line">                    curMax = i;</span><br><span class="line">                    <span class="keyword">break</span>; <span class="comment">// 找到就退出for</span></span><br><span class="line">                &#125;</span><br><span class="line">            &#125;</span><br><span class="line"></span><br><span class="line">            <span class="comment">// 2.</span></span><br><span class="line">            <span class="keyword">if</span> (<span class="keyword">this</span>-&gt;curPerm.<span class="built_in">at</span>(curPos) &gt;= curMax) <span class="comment">// 未找到位置移动</span></span><br><span class="line">            &#123;</span><br><span class="line">                flags.<span class="built_in">erase</span>(<span class="keyword">this</span>-&gt;curPerm.<span class="built_in">at</span>(curPos)); <span class="comment">// 哈希表减少</span></span><br><span class="line">                --curPos;</span><br><span class="line">            &#125;</span><br><span class="line">            <span class="keyword">else</span> <span class="comment">// 找到位置退出while</span></span><br><span class="line">            &#123;</span><br><span class="line">                <span class="keyword">break</span>;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="keyword">if</span> (curPos &lt; <span class="number">0</span>) <span class="comment">// 没找到位置搜完排列</span></span><br><span class="line">        &#123;</span><br><span class="line">            <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="comment">// 3.这个位置上的数值最小限度地增加—“最小限度”，前面的数值排除之后，取剩余的、大于该值的最小值</span></span><br><span class="line">        <span class="comment">// 从前往后小到大遍历，如果这个数不在哈希表中就是应该变换的值</span></span><br><span class="line">        <span class="comment">// 注意：此时可能处理左边的位置，哈希表还是删减状态以让左边位置可以取到右边的值</span></span><br><span class="line">        <span class="comment">// 如014，遍历012到2最小且不在哈希表，将索引1位置元素1换成2，该位置后续可以取到右边的值4，右边的值相应的会减小不再是4保证不重复</span></span><br><span class="line">        <span class="keyword">for</span> (<span class="type">int</span> i = <span class="keyword">this</span>-&gt;curPerm.<span class="built_in">at</span>(curPos); i &lt; <span class="keyword">this</span>-&gt;n; ++i)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="keyword">if</span> (flags.<span class="built_in">find</span>(i) == flags.<span class="built_in">end</span>())</span><br><span class="line">            &#123;</span><br><span class="line">                <span class="keyword">this</span>-&gt;flags.<span class="built_in">erase</span>(<span class="keyword">this</span>-&gt;curPerm.<span class="built_in">at</span>(curPos)); <span class="comment">// 哈希删除</span></span><br><span class="line">                <span class="keyword">this</span>-&gt;curPerm.<span class="built_in">at</span>(curPos) = i;</span><br><span class="line">                <span class="keyword">this</span>-&gt;flags.<span class="built_in">insert</span>(i); <span class="comment">// 哈希插入</span></span><br><span class="line">                <span class="keyword">break</span>;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="comment">// 归位哈希表。因为右边的数要填充了</span></span><br><span class="line">        <span class="comment">// 如034，位置1可以取到4，但此时哈希表是没有4的，将3变为4后，需要加入哈希表，右边的值填充时不能再是4，不是044而是041</span></span><br><span class="line">        <span class="keyword">for</span> (<span class="type">const</span> <span class="type">int</span> p : <span class="keyword">this</span>-&gt;curPerm)</span><br><span class="line">        &#123;</span><br><span class="line">            flags.<span class="built_in">insert</span>(p);</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="comment">// 4. 该位置确定后，后面的位置依次取剩余数值的最小几个</span></span><br><span class="line">        <span class="comment">// 对右边的所有位置</span></span><br><span class="line">        <span class="comment">// 从前往后小到大遍历，如果这个数不在哈希表中就是应该变换的值</span></span><br><span class="line">        <span class="comment">// 如024，遍历01到1最小且不在哈希表，</span></span><br><span class="line">        <span class="keyword">for</span> (<span class="type">int</span> i = curPos + <span class="number">1</span>; i &lt; <span class="keyword">this</span>-&gt;m; ++i)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">0</span>; j &lt; <span class="keyword">this</span>-&gt;n; ++j)</span><br><span class="line">            &#123;</span><br><span class="line">                <span class="keyword">if</span> (flags.<span class="built_in">find</span>(j) == flags.<span class="built_in">end</span>())</span><br><span class="line">                &#123;</span><br><span class="line">                    <span class="keyword">this</span>-&gt;flags.<span class="built_in">erase</span>(<span class="keyword">this</span>-&gt;curPerm.<span class="built_in">at</span>(i)); <span class="comment">// 哈希删除</span></span><br><span class="line">                    <span class="keyword">this</span>-&gt;curPerm.<span class="built_in">at</span>(i) = j;</span><br><span class="line">                    <span class="keyword">this</span>-&gt;flags.<span class="built_in">insert</span>(j); <span class="comment">// 哈希插入</span></span><br><span class="line">                    <span class="keyword">break</span>;</span><br><span class="line">                &#125;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        ++<span class="keyword">this</span>-&gt;permCount;</span><br><span class="line">        <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">printCurPerm</span><span class="params">()</span></span></span><br><span class="line"><span class="function">    </span>&#123;</span><br><span class="line">        <span class="keyword">for</span> (<span class="type">const</span> <span class="type">int</span> p : <span class="keyword">this</span>-&gt;curPerm)</span><br><span class="line">        &#123;</span><br><span class="line">            cout &lt;&lt; p &lt;&lt; <span class="string">&quot; &quot;</span>;</span><br><span class="line">        &#125;</span><br><span class="line">        cout &lt;&lt; endl;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">printPermCount</span><span class="params">()</span></span></span><br><span class="line"><span class="function">    </span>&#123;</span><br><span class="line">        cout &lt;&lt; <span class="keyword">this</span>-&gt;permCount &lt;&lt; endl;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line"><span class="keyword">private</span>:</span><br><span class="line">    <span class="type">const</span> <span class="type">int</span> n; <span class="comment">// 从n个取m个</span></span><br><span class="line">    <span class="type">const</span> <span class="type">int</span> m;</span><br><span class="line"></span><br><span class="line">    vector&lt;<span class="type">int</span>&gt; curPerm;      <span class="comment">// 当前排列，存储排列的索引</span></span><br><span class="line">    unordered_set&lt;<span class="type">int</span>&gt; flags; <span class="comment">// 哈希标志，标记已在排列中的索引</span></span><br><span class="line">    <span class="type">int</span> permCount;            <span class="comment">// 排列数的数量</span></span><br><span class="line">&#125;;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="type">const</span> <span class="type">int</span> n = <span class="number">5</span>;</span><br><span class="line">    <span class="type">const</span> <span class="type">int</span> m = <span class="number">3</span>;</span><br><span class="line">    <span class="function">CPermutation <span class="title">perm</span><span class="params">(n, m)</span></span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (perm.<span class="built_in">next</span>())</span><br><span class="line">    &#123;</span><br><span class="line">        perm.<span class="built_in">printCurPerm</span>();</span><br><span class="line">    &#125;</span><br><span class="line">    perm.<span class="built_in">printPermCount</span>();</span><br><span class="line"></span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<hr>
<h1 id="编译和运行命令"><a href="#编译和运行命令" class="headerlink" title="编译和运行命令"></a>编译和运行命令</h1><figure class="highlight powershell"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">g++ <span class="literal">-o</span> cpermutation cpermutation.cpp</span><br><span class="line">./cpermutation.exe</span><br></pre></td></tr></table></figure>
<hr>
<h1 id="结果"><a href="#结果" class="headerlink" title="结果"></a>结果</h1><p><img src= "" data-lazy-src="/../img/cpermutation/one.png" alt="在这里插入图片描述"></p>
<p><img src= "" data-lazy-src="/../img/cpermutation/two.png" alt="在这里插入图片描述"></p>
<hr>
<h1 id="总结"><a href="#总结" class="headerlink" title="总结"></a>总结</h1><p>C++代码示例：排列数简单生成工具。</p>
<hr>
<h1 id="参考资料"><a href="#参考资料" class="headerlink" title="参考资料"></a>参考资料</h1><ul>
<li>学校《高级算法设计与分析》课程课件的算法思路</li>
</ul>
<hr>
<h1 id="作者的话"><a href="#作者的话" class="headerlink" title="作者的话"></a>作者的话</h1><ul>
<li><strong>感谢参考资料的作者&#x2F;博主</strong></li>
<li>作者：夜悊</li>
<li>版权所有，转载请注明出处，谢谢~</li>
<li><strong>如果文章对你有帮助，请点个赞或加个粉丝吧，你的支持就是作者的动力~</strong></li>
<li>文章在描述时有疑惑的地方，请留言，定会一一耐心讨论、解答</li>
<li>文章在认识上有错误的地方, 敬请批评指正</li>
<li>望读者们都能有所收获</li>
</ul>
<hr>
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class="far fa-calendar-alt fa-fw"></i> 2023-10-02</div><div class="title">C++代码示例：进制数简单生成工具</div></div></a></div></div></div></div><div class="aside-content" id="aside-content"><div class="sticky_layout"><div class="card-widget" id="card-toc"><div class="item-headline"><i class="fas fa-stream"></i><span>目录</span><span class="toc-percentage"></span></div><div class="toc-content is-expand"><ol class="toc"><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%89%8D%E8%A8%80"><span class="toc-number">1.</span> <span class="toc-text">前言</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E4%BB%A3%E7%A0%81%E4%BB%93%E5%BA%93"><span class="toc-number">2.</span> <span class="toc-text">代码仓库</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%86%85%E5%AE%B9"><span class="toc-number">3.</span> <span class="toc-text">内容</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E4%BB%A3%E7%A0%81%EF%BC%88%E6%9C%89%E8%AF%A6%E7%BB%86%E6%B3%A8%E9%87%8A%EF%BC%89"><span class="toc-number">4.</span> <span class="toc-text">代码（有详细注释）</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E7%BC%96%E8%AF%91%E5%92%8C%E8%BF%90%E8%A1%8C%E5%91%BD%E4%BB%A4"><span class="toc-number">5.</span> <span class="toc-text">编译和运行命令</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E7%BB%93%E6%9E%9C"><span class="toc-number">6.</span> <span class="toc-text">结果</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E6%80%BB%E7%BB%93"><span class="toc-number">7.</span> <span class="toc-text">总结</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%8F%82%E8%80%83%E8%B5%84%E6%96%99"><span class="toc-number">8.</span> <span class="toc-text">参考资料</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E4%BD%9C%E8%80%85%E7%9A%84%E8%AF%9D"><span class="toc-number">9.</span> 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